Tori Noquez and Maxwell Levine : Model Theory of Real Closed Fields

Posted by Victoria Noquez , part of the Louise Hay Logic Seminar.

At

Sept. 20, 2012, 3 p.m.

In

SEO 427

Abstract

We will discuss the algebra of ordered fields, and use this to show that the theory of real closed fields admits quantifier elimination, and thus, is model complete in the language of ordered rings. From this, we prove that the theory of real closed fields is o-minimal, and give proofs of Hilbert's 17th problem and the Real Nullstellensatz.